Fixing Non-manifold edges for 3D printing
Non-manifold geometry is geometry where an edge is shared by more than 2 faces: 



This is what you should be looking for. It's easy to find using Select -> Select All by Trait -> Non Manifold 



Once you find it you can fix it by deleting some unnecessary faces, or separating the edges. You could use Edge split for that: 



Note that it splits  them all so you need to move one and then remerge the two you like connected(you can use Merge by Distance for that)